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Journal articles on the topic 'Self-adjoint operators'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Araujo, Vanilse S., F. A. B. Coutinho, and J. Fernando Perez. "Operator domains and self-adjoint operators." American Journal of Physics 72, no. 2 (February 2004): 203–13. http://dx.doi.org/10.1119/1.1624111.

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2

Podlevskii, B. M. "Self-adjoint polynomial operator pencils, spectrally equivalent to self-adjoint operators." Ukrainian Mathematical Journal 36, no. 5 (1985): 498–500. http://dx.doi.org/10.1007/bf01086780.

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3

Karabash, I. M., and S. Hassi. "Similarity between J-Self-Adjoint Sturm--Liouville Operators with Operator Potential and Self-Adjoint Operators." Mathematical Notes 78, no. 3-4 (September 2005): 581–85. http://dx.doi.org/10.1007/s11006-005-0159-z.

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4

Hiptmair, Ralf, Peter Robert Kotiuga, and Sébastien Tordeux. "Self-adjoint curl operators." Annali di Matematica Pura ed Applicata 191, no. 3 (February 25, 2011): 431–57. http://dx.doi.org/10.1007/s10231-011-0189-y.

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5

Molnár, Lajos, and Peter Šemrl. "Elementary operators on self-adjoint operators." Journal of Mathematical Analysis and Applications 327, no. 1 (March 2007): 302–9. http://dx.doi.org/10.1016/j.jmaa.2006.04.039.

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6

DAVIES, E. B. "NON-SELF-ADJOINT DIFFERENTIAL OPERATORS." Bulletin of the London Mathematical Society 34, no. 05 (September 2002): 513–32. http://dx.doi.org/10.1112/s0024609302001248.

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7

Toland, J. F. "Self-Adjoint Operators and Cones." Journal of the London Mathematical Society 53, no. 1 (February 1996): 167–83. http://dx.doi.org/10.1112/jlms/53.1.167.

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8

Miyao, Tadahiro. "Strongly Supercommuting Self-Adjoint Operators." Integral Equations and Operator Theory 50, no. 4 (December 2004): 505–35. http://dx.doi.org/10.1007/s00020-003-1233-0.

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9

Sebestyén, Zoltán, and Zsigmond Tarcsay. "Characterizations of essentially self-adjoint and skew-adjoint operators." Studia Scientiarum Mathematicarum Hungarica 52, no. 3 (September 2015): 371–85. http://dx.doi.org/10.1556/012.2015.52.3.1300.

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An extension of von Neumann’s characterization of essentially selfadjoint operators is given among not necessarily densely defined symmetric operators which are assumed to be closable. Our arguments are of algebraic nature and follow the idea of [1].

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10

Gomilko, A. M. "On the theory ofJ-self-adjoint perturbations of self-adjoint operators." Functional Analysis and Its Applications 30, no. 1 (January 1996): 47–49. http://dx.doi.org/10.1007/bf02509558.

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11

Kanguzhin,, Baltabek, Lyailya Zhapsarbayeva, and Zhumabay Madibaiuly. "LAGRANGE FORMULA FOR DIFFERENTIAL OPERATORS AND SELF-ADJOINT RESTRICTIONS OF THE MAXIMAL OPERATOR ON A TREE." Eurasian Mathematical Journal 10, no. 1 (2019): 16–29. http://dx.doi.org/10.32523/2077-9879-2019-10-1-16-29.

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12

Castillo, G. F. Torres Del, and J. C. Flores-Urbina. "Self-adjoint Operators and Conserved Currents." General Relativity and Gravitation 31, no. 9 (September 1999): 1315–25. http://dx.doi.org/10.1023/a:1026728925374.

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13

Derkach, Vladimir, Seppo Hassi, and Henk de Snoo. "Singular Perturbations of Self-Adjoint Operators." Mathematical Physics, Analysis and Geometry 6, no. 4 (April 2003): 349–84. http://dx.doi.org/10.1023/b:mpag.0000007189.09453.fc.

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14

Rooin, Jamal, A. Alikhani, and Mohammad Sal Moslehian. "Riemann sums for self-adjoint operators." Mathematical Inequalities & Applications, no. 3 (2014): 1115–24. http://dx.doi.org/10.7153/mia-17-83.

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15

Mironov, Andrey E. "Self-adjoint commuting ordinary differential operators." Inventiones mathematicae 197, no. 2 (October 19, 2013): 417–31. http://dx.doi.org/10.1007/s00222-013-0486-8.

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16

Döring, Andreas, and Barry Dewitt. "Self-adjoint Operators as Functions I." Communications in Mathematical Physics 328, no. 2 (April 12, 2014): 499–525. http://dx.doi.org/10.1007/s00220-014-1991-3.

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17

Goldstein, Daniel, and Robert M. Guralnick. "Alternating forms and self-adjoint operators." Journal of Algebra 308, no. 1 (February 2007): 330–49. http://dx.doi.org/10.1016/j.jalgebra.2006.06.009.

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18

Zheng, Shijun. "Interpolation theorems for self-adjoint operators." Analysis in Theory and Applications 25, no. 1 (March 2009): 79–85. http://dx.doi.org/10.1007/s10496-009-0079-y.

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19

Jung, Sungeun. "Properties of J-self-adjoint operators." Operators and Matrices, no. 2 (2021): 627–44. http://dx.doi.org/10.7153/oam-2021-15-42.

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20

Osipov, Andrey. "On unbounded commuting Jacobi operators and some related issues." Concrete Operators 6, no. 1 (January 1, 2019): 82–91. http://dx.doi.org/10.1515/conop-2019-0008.

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Abstract We consider the situations, when two unbounded operators generated by infinite Jacobi matrices, are self-adjoint and commute. It is found that if two Jacobi matrices formally commute, then two corresponding operators are either self-adjoint and commute, or admit a commuting self-adjoint extensions. In the latter case such extensions are explicitly described. Also, some necessary and sufficient conditions for self-adjointness of Jacobi operators are studied.

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21

Shangping, Liu. "Generalized functions associated with self-adjoint operators." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 68, no. 3 (June 2000): 301–11. http://dx.doi.org/10.1017/s1446788700001397.

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AbstractIn this paper, from several commutative self-adjoint operators on a Hilbert space, we define a class of spaces of fundamental functions and generalized functions, which are characterized completely by selfadjoint operators. Specially, using the common eigenvectors of these self-adjoint operators, we give the general form of expansion in series of generalized functions

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22

Ghaedrahmati, Arezoo, and Ali Sameripour. "Investigation of the Spectral Properties of a Non-Self-Adjoint Elliptic Differential Operator." International Journal of Mathematics and Mathematical Sciences 2021 (May 13, 2021): 1–7. http://dx.doi.org/10.1155/2021/5564552.

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Non-self-adjoint operators have many applications, including quantum and heat equations. On the other hand, the study of these types of operators is more difficult than that of self-adjoint operators. In this paper, our aim is to study the resolvent and the spectral properties of a class of non-self-adjoint differential operators. So we consider a special non-self-adjoint elliptic differential operator (Au)(x) acting on Hilbert space and first investigate the spectral properties of space H 1 = L 2 Ω 1 . Then, as the application of this new result, the resolvent of the considered operator in ℓ -dimensional space Hilbert H ℓ = L 2 Ω ℓ is obtained utilizing some analytic techniques and diagonalizable way.

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23

Hussein, Amru. "Sign-indefinite second-order differential operators on finite metric graphs." Reviews in Mathematical Physics 26, no. 04 (May 2014): 1430003. http://dx.doi.org/10.1142/s0129055x14300039.

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The question of self-adjoint realizations of sign-indefinite second-order differential operators is discussed in terms of a model problem. Operators of the type [Formula: see text] are generalized to finite, not necessarily compact, metric graphs. All self-adjoint realizations are parametrized using methods from extension theory. The spectral and scattering theories of the self-adjoint realizations are studied in detail.

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24

Petrosyan, Garik G. "On adjoint operators for fractional differentiation operators." Russian Universities Reports. Mathematics, no. 131 (2020): 284–89. http://dx.doi.org/10.20310/2686-9667-2020-25-131-284-289.

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On a linear manifold of the space of square summable functions on a finite segment vanishing at its ends, we consider the operator of left-sided Caputo fractional differentiation. We prove that the adjoint for it is the operator of right-sided Caputo fractional differentiation. Similar results are established for the Riemann–Liouville fractional differentiation operators. We also demonstrate that the operator, which is represented as the sum of the left-sided and the right-sided fractional differentiation operators is self adjoint. The known properties of the Caputo and Riemann–Liouville fractional derivatives are used to substantiate the results.

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25

Kudryashov, Yu L. "Dilatations of Linear Operators." Contemporary Mathematics. Fundamental Directions 66, no. 2 (December 15, 2020): 209–20. http://dx.doi.org/10.22363/2413-3639-2020-66-2-209-220.

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The article is devoted to building various dilatations of linear operators. The explicit construction of a unitary dilation of a compression operator is considered. Then the J -unitary dilatation of a bounded operator is constructed by means of the operator knot concept of a bounded linear operator. Using the Pavlov method, we construct the self-adjoint dilatation of a bounded dissipative operator. We consider spectral and translational representations of the self-adjoint dilatation of a densely defined dissipative operator with nonempty set of regular points. Using the concept of an operator knot for a bounded operator and the Cayley transform, we introduce an operator knot for a linear operator. By means of this concept, we construct the J -self-adjoint dilatation of a densely defined operator with a regular point. We obtain conditions of isomorphism of extraneous dilations and their minimality.

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26

Phillips, John. "Self-Adjoint Fredholm Operators And Spectral Flow." Canadian Mathematical Bulletin 39, no. 4 (December 1, 1996): 460–67. http://dx.doi.org/10.4153/cmb-1996-054-4.

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AbstractWe study the topology of the nontrivial component, , of self-adjoint Fredholm operators on a separable Hilbert space. In particular, if {Bt} is a path of such operators, we can associate to {Bt} an integer, sf({Bt}), called the spectral flow of the path. This notion, due to M. Atiyah and G. Lusztig, assigns to the path {Bt} the net number of eigenvalues (counted with multiplicities) which pass through 0 in the positive direction. There are difficulties in making this precise — the usual argument involves looking at the graph of the spectrum of the family (after a suitable perturbation) and then counting intersection numbers with y = 0.We present a completely different approach using the functional calculus to obtain continuous paths of eigenprojections (at least locally) of the form . The spectral flow is then defined as the dimension of the nonnegative eigenspace at the end of this path minus the dimension of the nonnegative eigenspace at the beginning. This leads to an easy proof that spectral flow is a well-defined homomorphism from the homotopy groupoid of onto Z. For the sake of completeness we also outline the seldom-mentioned proof that the restriction of spectral flow to is an isomorphism onto Z.

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27

Gómez, Fernando. "Self-adjoint time operators and invariant subspaces." Reports on Mathematical Physics 61, no. 1 (February 2008): 123–48. http://dx.doi.org/10.1016/s0034-4877(08)80004-3.

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28

El-Gebeily, M. A., Donal O’Regan, and Ravi Agarwal. "Characterization of self-adjoint ordinary differential operators." Mathematical and Computer Modelling 54, no. 1-2 (July 2011): 659–72. http://dx.doi.org/10.1016/j.mcm.2011.03.009.

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29

Pastur, L. A. "Spectral theory of random self-adjoint operators." Journal of Soviet Mathematics 46, no. 4 (August 1989): 1979–2021. http://dx.doi.org/10.1007/bf01096021.

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30

Laura Arias, M., and M. Celeste Gonzalez. "Products of projections and self-adjoint operators." Linear Algebra and its Applications 555 (October 2018): 70–83. http://dx.doi.org/10.1016/j.laa.2018.05.036.

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31

Phan, Quang Sang. "Spectral monodromy of non-self-adjoint operators." Journal of Mathematical Physics 55, no. 1 (January 2014): 013504. http://dx.doi.org/10.1063/1.4855475.

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32

Kappeler, Th. "Positive perturbations of self-adjoint Schrödinger operators." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 99, no. 3-4 (1985): 241–48. http://dx.doi.org/10.1017/s0308210500014268.

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SynopsisIn this paper, we prove that a positive perturbation T = T0 + q (q ≧ 0 and in ) of an essentially self-adjoint Schrödinger operator T0 = −Δ + q0 on is again essentially self-adjoint if T is relatively bounded with respect to T0. An application of the method of the proof to positive approximations of elements u ≧ 0 in D(T) by a positive sequence in is given.

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33

Wójcik, Paweł. "Self-adjoint operators on real Banach spaces." Nonlinear Analysis: Theory, Methods & Applications 81 (April 2013): 54–61. http://dx.doi.org/10.1016/j.na.2012.12.013.

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34

Schmüdgen, Konrad. "On Commuting Unbounded Self-Adjoint Operators, IV." Mathematische Nachrichten 125, no. 1 (1986): 83–102. http://dx.doi.org/10.1002/mana.19861250106.

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35

Davies, E. B. "Limits onLpRegularity of Self-Adjoint Elliptic Operators." Journal of Differential Equations 135, no. 1 (March 1997): 83–102. http://dx.doi.org/10.1006/jdeq.1996.3219.

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36

Green, Edward L. "Bounds on Perturbations of Self-Adjoint Operators." Journal of Mathematical Analysis and Applications 201, no. 2 (July 1996): 577–87. http://dx.doi.org/10.1006/jmaa.1996.0274.

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37

Kapustin, V. V. "Non-Self-Adjoint Extensions of Symmetric Operators." Journal of Mathematical Sciences 120, no. 5 (April 2004): 1696–703. http://dx.doi.org/10.1023/b:joth.0000018868.45777.a1.

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38

Kapitula, Todd, and Keith Promislow. "Stability indices for constrained self-adjoint operators." Proceedings of the American Mathematical Society 140, no. 3 (March 1, 2012): 865–80. http://dx.doi.org/10.1090/s0002-9939-2011-10943-2.

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39

DAMAK, MONDHER, and VLADIMIR GEORGESCU. "SELF-ADJOINT OPERATORS AFFILIATED TO C*-ALGEBRAS." Reviews in Mathematical Physics 16, no. 02 (March 2004): 257–80. http://dx.doi.org/10.1142/s0129055x04001984.

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We discuss criteria for the affiliation of a self-adjoint operator to a C*-algebra. We consider in particular the case of graded C*-algebras and we give applications to Hamiltonians describing the motion of dispersive N-body systems and the wave propagation in pluristratified media.

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40

Khrushchev, S. V. "Uniqueness theorems and essentially self-adjoint operators." Journal of Soviet Mathematics 36, no. 3 (February 1987): 403–8. http://dx.doi.org/10.1007/bf01839612.

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41

Bokhonov, Yu E. "Self-adjoint extensions of commuting Hermite operators." Ukrainian Mathematical Journal 42, no. 5 (May 1990): 614–16. http://dx.doi.org/10.1007/bf01065067.

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42

Arazy, Jonathan, and Leonid Zelenko. "Finite-dimensional perturbations of self-adjoint operators." Integral Equations and Operator Theory 34, no. 2 (June 1999): 127–64. http://dx.doi.org/10.1007/bf01236469.

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43

Balasubramanian, Venkat, Saurya Das, and Elias C. Vagenas. "Generalized uncertainty principle and self-adjoint operators." Annals of Physics 360 (September 2015): 1–18. http://dx.doi.org/10.1016/j.aop.2015.04.033.

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44

Gubreev, G. M., and A. A. Tarasenko. "On the similarity to self-adjoint operators." Functional Analysis and Its Applications 48, no. 4 (December 2014): 286–90. http://dx.doi.org/10.1007/s10688-014-0071-y.

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45

Aleksandrov, Aleksei, Fedor Nazarov, and Vladimir Peller. "Functions of perturbed noncommuting self-adjoint operators." Comptes Rendus Mathematique 353, no. 3 (March 2015): 209–14. http://dx.doi.org/10.1016/j.crma.2014.12.005.

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46

Tari, Farid. "Self-adjoint operators on surfaces in Rn." Differential Geometry and its Applications 27, no. 2 (April 2009): 296–306. http://dx.doi.org/10.1016/j.difgeo.2008.10.010.

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47

Dubrovskii, V. V. "Regularized traces of non-self-adjoint operators." Mathematical Notes 67, no. 2 (February 2000): 266. http://dx.doi.org/10.1007/bf02686258.

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48

Neidhardt, Hagen, and Valentin A. Zagrebnov. "On semibounded restrictions of self-adjoint operators." Integral Equations and Operator Theory 31, no. 4 (December 1998): 489–512. http://dx.doi.org/10.1007/bf01228105.

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49

Burenkov, V. I., P. D. Lamberti, and M. Lanza de Cristoforis. "Spectral stability of nonnegative self-adjoint operators." Journal of Mathematical Sciences 149, no. 4 (March 2008): 1417–52. http://dx.doi.org/10.1007/s10958-008-0074-4.

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50

Cuenin, Jean-Claude, and Christiane Tretter. "Non-symmetric perturbations of self-adjoint operators." Journal of Mathematical Analysis and Applications 441, no. 1 (September 2016): 235–58. http://dx.doi.org/10.1016/j.jmaa.2016.03.070.

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